Right and East
Lake Michigan is to the East of Chicago or to your right if you're facing north.
north east
You would have to go north to reach Lake Michigan.
east
You would travel east. However, if you were in Chicago Heights, you would travel north. If you were in East Chicago, you could travel north or east.
You would go to the east which would be to your right.
Chicago, Illinois, is on the southwestern shore of Lake Michigan. Therefore, Lake Michigan is in an easterly or northeasterly direction from central Chicago.
Right then East
Right then East
You would need to turn right to head eastward to Lake Michigan.
If you are in Milwaukee, Wisconsin facing north, you would go east to Lake Michigan.
You would travel East or to your right. In a more detailed explanation you would go north east.